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categoryرياضيات
schoolبكالوريوس
event_available2026-07-13
السؤال
Transcribed Image Text:
Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t.
x' = 2x-y
y' = 2y-16x
Eliminate x and solve the remaining differential equation for y. Choose the correct answer below.
A. y(t) = C₁ e 2 + C₂e 6t
OB. y(t)=C₁e
21+ C₂ e - 6t
OC. y(t)=C₁e e6t + C₂te 6
OD. y(t) = C₁e 2 + C₂te
-21
E. The system is degenerate.
Now find x(t) so that x(t) and the solution for y(t) found in the previous step are a general solution to the system of differential equations. Select the correct choice
below and, if necessary, fill in the answer box to complete your choice.
A. x(t)=C₁e
-21
6t
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